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The mean value theorem and Taylor’s theorem for fractional derivatives with Mittag–Leffler kernel [PDF]
Advances in Difference Equations, 2018 We establish analogues of the mean value theorem and Taylor’s theorem for fractional differential operators defined using a Mittag–Leffler kernel. We formulate a new model for the fractional Boussinesq equation by using this new Taylor series expansion.
Arran Fernandez, Dumitru Baleanu
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On Generalized Flett's Mean Value Theorem [PDF]
International Journal of Mathematics and Mathematical Sciences, 2012 We present a new proof of generalized Flett's mean value theorem due to Pawlikowska (from 1999) using only the original Flett's mean value theorem. Also, a Trahan-type condition is established in general case.
Jana Molnárová
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On Flett’s mean value theorem [PDF]
Aequationes mathematicae, 2014 Mean value theorems play an important role in differential and integral calculus as they are a powerful tool for solving problems in mathematical analysis. The authors of the present paper provide a thorough study of Flett's mean value theorem of a real-valued function of one real variable.
Hutník, Ondrej, Molnárová, Jana
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Some variants of Lagrange’s mean value theorem
Selecciones Matemáticas, 2020 In this note we prove some variants of Lagrange’s mean value theorem. The main tools to prove these results are some elementary auxiliary functions.
German Lozada-Cruz
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The Mean Value Theorem in the Context of Generalized Approach to Differentiability
Mathematics, 2023 The article is a natural continuation of the systematic research of the properties of the generalized concept of differentiability for functions with a domain X⊂Rn that is not necessarily open, at points that allow a neighbourhood ray in the domain.
Nikola Koceić-Bilan +1 more
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On some mean value theorem via covering argument
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2020 We show how the full covering argument can be used to prove some type of Cauchy mean value theorem.
Sokołowski Dariusz
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A General Mean-Value Theorem [PDF]
Transactions of the American Mathematical Society, 1924 In a paper published in 1906t, Professor G. D. Birkhoff treated the meanvalue and remainder theorems belonging to polynomial interpolation, in which the linear differelntial operator lt(n) played a particular role. It is natural to expect that a generalization of many of the ideas of that paper may apply to the general linear differential operator of ...
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Sensitivity of the “intermediate point” in the mean value theorem: an approach via the Legendre-Fenchel transformation [PDF]
ESAIM: Proceedings and Surveys, 2021 We study the sensitivity, essentially the differentiability, of the so-called “intermediate point” c in the classical mean value theorem fa-f(b)b-a=f'(c)$ \frac{f(a)-f(b)}{b-a}={f}^{\prime}(c)$we provide the expression of its gradient ∇c(d,d), thus ...
Hiriart-Urruty Jean-Baptiste
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A general mean value theorem [PDF]
Publicationes Mathematicae Debrecen, 2016 In this note a general a Cauchy-type mean value theorem for the ratio of functional determinants is offered. It generalizes Cauchy's and Taylor's mean value theorems as well as other classical mean value theorems.
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Mean Value Theorems on Manifolds [PDF]
Asian Journal of Mathematics, 2007 We derive several mean value formulae on manifolds, generalizing the classical one for harmonic functions on Euclidean spaces as well as later results of Schoen-Yau, Michael-Simon, etc, on curved Riemannian manifolds. For the heat equation a mean value theorem with respect to `heat spheres' is proved for heat equation with respect to evolving ...
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